2013
DOI: 10.1063/1.4812325
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Abstract: The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.

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Cited by 14 publications
(17 citation statements)
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“…Other practical outcome concerns the handling of the associated integrals and of many other technicalities related to the Ramanujan Master Theorem (RMT) 1 [1,2]. Furthermore, the same formalism provides the possibility of recovering a large body of the properties of Bessel functions and of other special functions as well, using genuine algebraic tools [5,6].…”
Section: Umbral Methods and The Negative Derivative Formalismmentioning
confidence: 99%
See 3 more Smart Citations
“…Other practical outcome concerns the handling of the associated integrals and of many other technicalities related to the Ramanujan Master Theorem (RMT) 1 [1,2]. Furthermore, the same formalism provides the possibility of recovering a large body of the properties of Bessel functions and of other special functions as well, using genuine algebraic tools [5,6].…”
Section: Umbral Methods and The Negative Derivative Formalismmentioning
confidence: 99%
“…Such a restyling allows noticeable simplifications in the theory of Bessel functions themselves [5,6]. Other practical outcome concerns the handling of the associated integrals and of many other technicalities related to the Ramanujan Master Theorem (RMT) 1 [1,2].…”
Section: Umbral Methods and The Negative Derivative Formalismmentioning
confidence: 99%
See 2 more Smart Citations
“…From the dynamical point of view the equation describes a spatial diffusion in a homogeneous medium (the coefficient D is assumed to be independent of the spatial coordinate) embedded with a growth of logistic nature [4].The coefficients r and K are the growth rate and the carrying capacity of the environment respectively [4]. If the process is purely diffusive (r = 0), the solution of our evolution problem is just provided by the following Gauss Weierstrass transform [5] …”
Section: Introductionmentioning
confidence: 99%